Long-time behavior of one-dimensional compressible Bingham flows

Barotropic flows of one-dimensional compressible Bingham fluids are considered. Long-time behavior of the corresponding initial-boundary problem is investigated. The uniform upper and lower bounds for the density and a decay of the kinetic energy are established. We admit a class of mass forces not considered for similar problems to Newtonian fluids. Under additional assumptions on the mass force, we achieve strong estimates for the solution (uniformly in time) and decays of the velocity and its derivatives. Received: April 14, 2004; revised: November 22, 2004